Many manufactured parts are formed by rotating blank stock about a fixed linear axis while adding or subtracting material. The resulting parts are referred to as "solids of revolution." Examples include a clay pot produced on a rotating wheel, a baseball bat shaped on a lathe, or a silicon crystal grown from a rotating seed dipped into a silicon melt. Once a solid of revolution has been formed, it may be used directly as in the case of a baseball bat. Alternatively, it may be used as a template from which copies are made through various means such a plastic or metal casting. Such copies, having been formed without the aid of a rotating axis, will nonetheless also be well described as solids of revolution by virtue of their shape.
A manufactured solid of revolution can be described by its profile which must generally conform to precise dimensional specifications. To ensure that the part conforms, and to avoid wasting material, a measurement of the radial dimension at various points along the axis of the part can be performed as the part is coming into being. This measurement can be performed in a variety of ways. For example, it is common to place a caliper in contact with the part to measure the diameter of the part immediately subsequent to a machining operation as the work progresses.
Each of these measurement methods represents contact-based measurement. However, there are some manufacturing situations where contact-based measurement methods present significant disadvantages. For example, machining operations typically generate an abundance of heat, and consequently, the part becomes quite hot at and near the site on the part where the machining operation is occurring. To this heat is added any frictionally generated heat from moving contact of the lever arm or caliper with the rotating part. Since heat can cause thermal expansion, the resulting dimensional instability of the measurement device can lead to measurement inaccuracy. In other manufacturing situations, the part may be made from a radioactive, chemically active, pressure sensitive, thermally sensitive, or ultra-pure material, and consequently it is desirable to minimize or eliminate any contact with the part. In these and other situations, it can be advantageous to use a non-contacting method for measuring the diameter of a part at various positions along the length of the part, and/or at various times during the manufacturing process.
A common non-contact approach for gauging parts described as solids of revolution involves viewing the object with a camera whose line-of-sight is normal to the object's axis of revolution. The resulting image then directly depicts the part profile. However, in order to obtain an accurate profile image, expensive optics must be used (e.g. telecentric lens) to achieve an image that well approximates an orthographic projection. Furthermore, this approach places strong constraints on camera position and viewing angle which are not always possible to achieve.
An important application where it is necessary to gauge a solid of revolution is in the production of mono-crystalline material used in the manufacture of semiconductor devices. Such crystals are grown in a sealed vacuum chamber to prevent exposure of the molten silicon to reactive gasses such as oxygen which would ruin the crystal. Given the severe conditions within the chamber, it is highly desirable to employ a non-contacting method to measure the dimensions of the crystalline material as it is being manufactured. However, the non-contacting approach described in the previous paragraph, involving orthographic profile projection is not feasible because it is not generally possible to arrange for the camera to view normal to the axis of revolution of the growing crystal. Rather, the camera must view the crystal from a oblique angle determined by the position of a small quartz viewing window built into the vacuum chamber within which the crystal is grown. Under these circumstances, visual gauging methods must be compatible with whatever view of the crystal happens to be available.
The manufacture of crystalline material is an important first step in the production of many products (laser, electronic chips, etc.). One widely used method for growing single large single crystals is known as "high temperature Czochralski crystal growth." This method is used, for example, to manufacture large crystals of Gallium Arsenide and Silicon. These crystals are then sliced to provide large wafers for use in the production of electronic chips.
FIG. 1 provides a simplified diagram of a Czochralski crystal growing system. The Czochralski crystal growing method involves lowering a single-crystalline "see crystal" 10 until it touches the surface of a high temperature melt of source material 12. The seed crystal 10 is continuously rotated and slowly pulled upward as material from the melt 12 adds to the length and diameter of the growing crystal. The seed 10, neck 14, crown 16, and body 18 are all parts of the growing crystal. The growing crystal is pulled 32 and rotated 34 via a chuck 20 attached to a cable 22 that is connected to a drive motor 24. The high temperature melt of source material 12 is contained in a crucible 26 that is heated by a heater 28. Gradually, over many hours, a single large crystal with an elongated body 18 is pulled from the melt 12.
To produce high quality crystals, it is necessary to continuously monitor the cross-section of the crystal body 18 where it contacts the melt 12. During early stages of crystal growth, the cross-section of the neck 14 and crown 16 must be similarly monitored. In practice, the crystal/melt contact is often visible as a bright meniscus 30 that extends just above the plane of the melt surface to contact the underside of the growing crystal. The meniscus 30 arises from surface tension and it appears bright because its curved surface strongly reflects light emitted by the hot wall of the crucible 26 used to contain the molten source material. Even when a meniscus is not present, for example during the crown stage of crystal growth, the boundary between crystal and melt is still generally visible as an abrupt change in luminance at the boundary.
The meniscus 30 can be used to estimate the crystal cross-sectional diameter. Known systems for estimating crystal diameter include systems that use a line-scan camera to sense luminance along a one-dimensional cross-section of the scene. The viewing angle of the camera is set to include the crystal and the melt to either side of the crystal. These systems all work by measuring the length of a chord that crosses the elliptical projection of the circular boundary between crystal and melt. By calibrating the relationship between chord length and crystal diameter, such systems have long been used to obtain a time-varying estimate of crystal diameter.
A major limitation of line-scan systems is due to their inability to distinguish between various factors, in addition to crystal diameter, that can cause the measured chord length to vary. These factors include changes in melt level, and changes in crystal position.
Melt level changes occur due to incorporation of molten source material into the solid crystal. The crucible may be gradually raised in an effort to maintain a constant melt level. However, melt level variation ranks as the largest source of error in the diameter estimates produced by line-scan systems.
The crystal position varies because the crystal is suspended by a long cable or rod that continuously rotates, causing the crystal to also rotate. Due to the rotational energy being imparted to the crystal, any minor disturbance tends to cause the crystal to oscillate, or orbit, about the central vertical axis of the puller in a pendulum-like fashion. The amplitude of such oscillations can be larger than the entire diameter of the crystal during the early stages of crystal growth, causing the line scan system to see no only large variations in chord length but also the complete disappearance of the crystal from its one-dimensional view. Therefore, line-scan systems perform badly during the early (neck and crown) stages of crystal growth.
The above limitations of line-scan systems for crystal diameter estimation can be overcome by two-dimensional imaging systems that detect and use the entire boundary defining the crystal/melt interface. Indeed, this interface is a rich source of information which is not fully exploited in existing systems, even when these systems employ a two-dimensional image sensor. For example, on existing system sold by Hamamatsu, requires a one-dimensional cross-section of the image in a manner that mimics the operation of a line-scan camera as describe above.
Another existing system, previously developed by Cognex Corporation, Natick, Ma., the assignee of the present invention, acquires a two-dimensional image from which it estimates the width (in pixels) of the elliptical projection of the crystal meniscus. That Cognex system effectively deals with crystal orbit, but is unable to tell if a change in projection width results from a change in melt level or a true change in crystal diameter.